PySensors is a Python package for selecting and placing a sparse set of sensors for reconstruction and classification tasks. In this major update to PySensors, we introduce spatially constrained sensor placement capabilities, allowing users to enforce constraints such as maximum or exact sensor counts in specific regions, incorporate predetermined sensor locations, and maintain minimum distances between sensors. We extend functionality to support custom basis inputs, enabling integration of any data-driven or spectral basis. We also propose a thermodynamic approach that goes beyond a single "optimal" sensor configuration and maps the complete landscape of sensor interactions induced by the training data. This comprehensive view facilitates integration with external selection criteria and enables assessment of sensor replacement impacts. The new optimization technique also accounts for over- and under-sampling of sensors, utilizing a regularized least squares approach for robust reconstruction. Additionally, we incorporate noise-induced uncertainty quantification of the estimation error and provide visual uncertainty heat maps to guide deployment decisions. To highlight these additions, we provide a brief description of the mathematical algorithms and theory underlying these new capabilities. We demonstrate the usage of new features with illustrative code examples and include practical advice for implementation across various application domains. Finally, we outline a roadmap of potential extensions to further enhance the package's functionality and applicability to emerging sensing challenges.

Given harsh operating conditions and physical constraints in reactors, nuclear applications cannot afford to equip the physical asset with a large array of sensors. Therefore, it is crucial to carefully determine the placement of sensors within the given spatial limitations, enabling the reconstruction of reactor flow fields and the creation of nuclear digital twins. Various design considerations are imposed, such as predetermined sensor locations, restricted areas within the reactor, a fixed number of sensors allocated to a specific region, or sensors positioned at a designated distance from one another. We develop a data-driven technique that integrates constraints into an optimization procedure for sensor placement, aiming to minimize reconstruction errors. Our approach employs a greedy algorithm that can optimize sensor locations on a grid, adhering to user-defined constraints. We demonstrate the near optimality of our algorithm by computing all possible configurations for selecting a certain number of sensors for a randomly generated state space system. In this work, the algorithm is demonstrated on the Out-of-Pile Testing and Instrumentation Transient Water Irradiation System (OPTI-TWIST) prototype vessel, which is electrically heated to mimic the neutronics effect of the Transient Reactor Test facility (TREAT) at Idaho National Laboratory (INL). The resulting sensor-based reconstruction of temperature within the OPTI-TWIST minimizes error, provides probabilistic bounds for noise-induced uncertainty and will finally be used for communication between the digital twin and experimental facility.

Ever since the introduction of Watkins' Q-learning algorithm in the 1980s, the research community has searched for a general theory beyond the so-called tabular settings (in which the function class spans all possible functions of state and action). The natural extension of Q-learning to general function approximation setting seeks to solve what is known as a projected Bellman equation (PBE). There are few results available giving sufficient conditions for the existence of a solution, or convergence of the algorithm if a solution does exist [24, 17, 10]. Counterexamples show that conditions on the function class are required in general, even in a linear function approximation setting [1, 25, 6]. The GQ-algorithm of [14] is one success story, based on a relaxation of the PBE. Even if existence and stability of the algorithm were settled, we would still face the challenge of interpreting the output of a Q-learning algorithm based on the PBE criterion.

Deep Reinforcement Learning is a promising paradigm for robotic control which has been shown to be capable of learning policies for high-dimensional, continuous control of unmodeled systems. However, RoboticReinforcement Learning currently lacks clearly defined benchmark tasks, which makes it difficult for researchers to reproduce and compare against prior work. ``Reacher'' tasks, which are fundamental to robotic manipulation, are commonly used as benchmarks, but the lack of a formal specification elides details that are crucial to replication. In this paper we present a novel empirical analysis which shows that the unstated spatial constraints in commonly used implementations of Reacher tasks make it dramatically easier to learn a successful control policy with DeepDeterministic Policy Gradients (DDPG), a state-of-the-art Deep RL algorithm. Our analysis suggests that less constrained Reacher tasks are significantly more difficult to learn, and hence that existing de facto benchmarks are not representative of the difficulty of general robotic manipulation.

One of the major aspects of training your machine learning model is avoiding overfitting. The model will have a low accuracy if it is overfitting. This happens because your model is trying too hard to capture the noise in your training dataset. By noise we mean the data points that don't really represent the true properties of your data, but random chance. Learning such data points, makes your model more flexible, at the risk of overfitting.

One of the major aspects of training your machine learning model is avoiding overfitting. The model will have a low accuracy if it is overfitting. This happens because your model is trying too hard to capture the noise in your training dataset. By noise we mean the data points that don't really represent the true properties of your data, but random chance. Learning such data points, makes your model more flexible, at the risk of overfitting. The concept of balancing bias and variance, is helpful in understanding the phenomenon of overfitting.

Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. We propose a new method called Hexagonal Operator for Regression with Shrinkage and Equality Selection, HORSES for short, that simultaneously selects positively correlated variables and identifies them as predictive clusters. This is achieved via a constrained least-squares problem with regularization that consists of a linear combination of an L_1 penalty for the coefficients and another L_1 penalty for pairwise differences of the coefficients. This specification of the penalty function encourages grouping of positively correlated predictors combined with a sparsity solution. We construct an efficient algorithm to implement the HORSES procedure. We show via simulation that the proposed method outperforms other variable selection methods in terms of prediction error and parsimony. The technique is demonstrated on two data sets, a small data set from analysis of soil in Appalachia, and a high dimensional data set from a near infrared (NIR) spectroscopy study, showing the flexibility of the methodology.